July 4, 2012


Series of straight lines could form a curve when the edges are smoothed out. It does not actually form the curve but approximates its form. The curve being formed is usually a parabola - that is why they sometimes call it as a parabolic curve. 

Let us discover how these curves are formed from the straight lines starting with the basics. 

What you need are:
1. paper (you can have a white paper or a colored paper of your choice)
2. pencil, marker or any colored writing material
3. ruler

STEP 1: The basic curve formation starts with two lines intersecting at a point. One is vertical and the other is horizontal. The lines resembles the positive x- and y- axes of the Cartesian plane that bound the first quadrant. 
STEP 2: Put dots or marks on the lines. Make sure that they have equal intervals. You may use the a rule to determine the intervals. Make sure also that there are equal number of dots for the two lines. The dots will be paired so there will be a dot left out if the number of dots are unequal.  
STEP 3: Pair the dots by connecting them using a line. Start with the uppermost dot in the vertical line paired with the leftmost dot in the horizontal line. You may also start with the rightmost dot of the horizontal line paired with the lowermost dot of the horizontal line. Any of these would yield to the same sets of lines. 
STEP 4: Continue with the same process until you paired all of the dots
The final output is this figure. Observe that a curve is approximated by the lines.

You may also use other colors for the set of lines.
You can also try combining the figures formed above like these:   
 You can also form figures like these:

The above figures used perpendicular lines. You can make the curve narrower by decreasing the angle being formed by the two lines. 

Aside from the perpendicular lines, you can also use other shapes or polygons like a square or a circle. You can try using a triangle, a pentagon, a hexagon and so on. 
I have tried combining the figures and formed this:
You can be creative in forming figures like this using the curves. Share it here after creating one. Have fun creating your work of art!


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